Haar Compression for Efficient CQI Feedback Signaling in 3GPP LTE Systems

Research Paper / Jan 2008

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Haar Compression for Efficient CQI Feedback Signaling in 3GPP LTE Systems

Research Paper / Jan 2008

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Haar Compression for Efficient CQI Feedback

Signaling in 3GPP LTE Systems

Afshin Haghighat, Zinan Lin and Guodong Zhang

afshin.haghighat, zinan.lin, guodong.zhang@interdigital.com

InterDigital Communications

Abstract— Frequency selective scheduling is an attractive

feature in the 3GPP LTE system that allows optimum usage of

the allocated spectrum. In order to support frequency selective

scheduling in the downlink, the mobile user needs to feedback

channel quality indication (CQI) of the downlink channel to the

base station. Several CQI feedback scheme have been proposed

for 3GPP LTE systems. We propose to apply Haar compression

to distributed subband groups to reduce the CQI feedback

overhead. The simulation results indicate that the distributed-

Haar scheme achieves the best trade-off between the

throughput performance and overhead reduction compared

with other CQI feedback schemes. We also observe that the

sensitivity in sector throughput performance to user mobility is

approximately the same for all feedback methods considered in

the paper.

Index Terms—Haar, CQI, LTE, feedback, frequency

selective scheduling.

I. INTRODUCTION

The 3GPP Long Term Evolution (LTE) technology

improves the capacity, coverage and flexibility of the

cellular system significantly beyond the existing 2G and 3G

cellular system technologies [1]. In order to realize such

enhancements, there have been several fundamental changes

in the system definitions and requirements in all layers of

the system [2]. One striking difference in the physical layer

of the system is the use of OFDMA as air interface instead

of WCDMA in the 3G UMTS systems. OFDMA offers

higher capacity and robust performance in a multipath

frequency selective mobile channel.

In 3G WCDMA HSDPA systems, since WCDMA is a

single-carrier system, only a single CQI is reported for each

H-ARQ process. Hence, the overhead associated with CQI

reporting is relatively small. On the other hand, in LTE

systems frequency selective scheduling is used to achieve

efficient usage of the spectrum. The unit used for frequency

selective scheduling is a sub-band, which includes a number

of consecutive subcarriers. To fully support the frequency

selective scheduling, ideally each mobile user needs to

report a set of CQI values, one for each sub-band. However,

this will lead to overwhelming large CQI feedback

overhead. In the current LTE standards, a budget of

approximately 10 bits per Transmission Time Interval (TTI)

for CQI feedback is being considered. Although this number

may be refined in the future, it provides an insight on the

range of the allowed feedback overhead for the CQI

feedback.

This challenge of designing a CQI feedback scheme that

achieves efficient usage of spectrum with reasonably low

overhead has spurred some research interests. Numerous

CQI reporting and compression schemes have been

proposed with different levels of compression and system

performance [3]-[5]. The proposed schemes can be divided

into two categories. The schemes in the first category

compress the CQI information of all the sub-bands in the

entire cell bandwidth and report the compressed CQI

information to the base station. An example of the schemes

in this category is DCT significant-M feedback scheme [3].

The second category includes techniques that are based on

reporting of only limited number of the highest CQIs among

all subbands, such as Best-M individual, DCT-partitioning.

The effectiveness of these methods varies and each has its

own inherent trade-off in terms of performance and

feedback overhead. Descriptions of other CQI feedback

reporting schemes that are referenced and compared to in the

simulations can be found in [3]-[5].

The techniques discussed in this paper hinges on the

principle of the latter category. We propose to further reduce

signaling overhead for the CQI feedback by applying Haar

compression to distributed groups of sub-bands. The

proposed distributed-Haar CQI feedback scheme supports a

flexible trade-off between system performance and CQI

feedback signaling overhead.

The rest of the paper is organized as follows: at first in

Section II, the 3GPP LTE system is briefly described. Then,

a review of Haar compression and the Best-M Haar CQI

reporting scheme is provided in Sections III and IV. Then, in

order to further reduce the overhead feedback, the

distributed-Haar CQI reporting scheme is introduced in

Section V. The performance of the distributed-Haar CQI

reporting scheme is simulated and compared with other

methods such as Best-M, DCT significant, and DCT

Partitioning in Section VI. Finally, the paper is concluded in

section VII.

II. SYSTEM DESCRIPTION

The diagram of the downlink OFDMA air interface in the

LTE system is shown in Figure 1. In the OFDMA system,

modulated bits are converted from serial to parallel first, and

then mapped to different subcarriers. After IFFT, the output

signals are converted back to serial signals called an OFDM

symbol. Cyclic prefix (CP) is attached to the beginning of

the OFDM symbol before transmission. Subcarrier spacing

of 15 kHz is used in the 3GPP LTE system. The time in the

3GPP LTE system is divided into radio frames. Each radio

frame (10 ms) is divided into 10 sub-frames of 1 ms each. A

sub-frame is the minimum time unit for transmission in both

uplink and downlink. Therefore, a sub-frame is also called a

TTI.

Figure 1: OFDMA air interface in 3GPP LTE systems.

The basic concept of frequency selective scheduling in the

3GPP LTE systems is depicted in Figure 2. Each UE needs

to estimate the channel quality and report the CQI of

downlink sub-bands to the base station. Then, the base

station schedules and allocates sub-bands for mobile users

based on reported CQI. The modulation and coding set

(MCS) of each scheduled user is also adapted according to

the reported CQI.

Figure 2: Frequency selective scheduling in the LTE

systems.

III. HAAR COMPRESSION

Haar compression is based on the Haar wavelet transform.

Detailed description of the Haar compression method can be

found in [6]-[7]. Haar compression encodes an input stream

in multiple steps according to the level of the detail of the

input sequence. Haar compression belongs to the class of

lossy compression methods, and it is recognized as an

effective and low complexity compression/decompression

means for processing 1- or 2-dimensional data.

The main idea of using the Haar transform to compress a

data vector is to shift the weight and importance of the

vector elements to the first element of the vector. The

process can be explained by an example as follows. Let the

input vector y be:

[ ]921151428312=y (1)

Since the vector has 23 elements, the transformation takes

3 steps of sum and difference operations as follows: first,

group the elements of the vector y in groups of 2’s. Find the

sum and the difference terms for each group and divide the

results by two. The results are now in a new vector y1.

[ ]

[ ]

[ ]3.5374.51.256.25.75y

3.5374.51.256.75y

3.5374.5y

−−−=

−−−=

−−=

35.10

75.625.14

5.58215.7

3

2

1

(2)

The first four elements of the vector y1 are called

“Approximate” and the last four elements, in Bold, are

called “Detail” coefficients. Steps 2 and 3 are similar to step

1, with the only difference being that they apply only on the

“Approximate” coefficients, while the “Detail” coefficients

are maintained to the end. As shown in Equation 2, the final

compressed vector is comprised of one “Approximate”

coefficient along with seven “Detail” coefficients.

In an abstract form, for a vector length equal to 8, the

successive averaging and differencing steps involved in the

compression process can be mathematically expressed as

( ) ( ) ( )[ ] 83333 178 yWy == yyy L (3)

where

.

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎥

⎦

⎤

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎢

⎣

⎡

=

−

−

−−

−−

−

−

−

−

−

−

2

1

2

1

2

1

2

1

4

1

8

1

8

1

4

1

8

1

8

1

4

1

8

1

8

1

4

1

8

1

8

1

2

1

2

1

2

1

2

1

4

1

8

1

8

1

4

1

8

1

8

1

4

1

8

1

8

1

4

1

8

1

8

1

8

000

000

000

000

0

0

0

0

000

000

000

000

0

0

0

0

W

(4)

1- Schedule the user and allocate sub-bands

2- Assign the proper MCS

1- Estimate the channel quality

2- Report CQI of sub-bands

Therefore, the decompression can be easily implemented by

83Fyy = , (5)

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎥

⎦

⎤

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎢

⎣

⎡

−

−

−

−

−−

−−−−

−−

== −

1100

0011

0000

0000

0000

0000

1100

0011

1111

0000

1111

1111

0000

1111

1111

1111

1

88 WF . (6)

It is worth mentioning that due to the particular value of

the coefficients for the compression and the decompression,

all the required multiplications can be performed by simple

shift-add functions in binary domain. Also, half of the

matrix elements are zeros. The two features result in a very

low complexity for compression and decompression

functions.

IV. BEST-M HAAR CQI FEEDBACK SCHEME

In [8], we proposed the best-M Haar CQI feedback

scheme for the 3GPP LTE systems. For a system with Nsb

sub-bands, the procedure for the proposed Haar-based

compression of the best M sub-bands’s CQI is as follows:

1. Select the M largest CQIs among all sub-bands.

2. Calculate the average CQI of remaining sub-bands

( ). AvgCQI

3. Create a vector comprising the M CQI values and

the . Hence, the total number of CQIs to be

reported in steps 1 and 2 is M+1. The Best-M CQI

values are reported in the same order as their relevant

sub-bands. The length of the input vector for Haar

compression is 2

AvgCQI

m, where m is the smallest integer to

satisfy (M+1) ≤ 2m. However, assuming a common

implementation structure, m could be larger than what is

specified earlier. The vector y will have 2m-(M+1) zeros

at predefined locations. For example, given an input

vector with a fixed length of 8,

For M = 3:

[ ]0000 321 AvgCQICQICQICQI=y ; (7)

For M = 4:

[ ]000 4321 AvgCQICQICQICQICQI=y ; (8)

For M = 5:

[ ]005421 AvgCQICQICQICQICQI L=y ; (9)

For M = 7:

[ ]AvgCQICQICQICQICQI 7621 L=y . (10)

If 5 bits are used to represent one CQI value in the

feedback, the vector will contain 5(M+1) bits of

information.

4. Apply the Haar transform as in Equation 3.

5. In step 3, if (M+1)<2m then zero insertion will be

implemented. However, after the compression,

according to the position of the inserted zeros, certain

elements of the compressed vector can be dropped

without any loss of information. For example, the last

four, three and two elements of the compressed vector

y3 become irrelevant for transmission and can be

dropped, for M=3, 4 and 5 respectively.

6. Quantize and send the remaining elements of the vector.

7. Send the location information of the Best-M sub-bands.

The number of bits required for the location information

is determined by

⎟⎟⎠

⎞

⎜⎜⎝

⎛

⎟⎟⎠

⎞

⎜⎜⎝

⎛=

M

N

N sbLocation 2log (11)

Each element of the compressed vector has a statistical

distribution that can be exploited to optimize the

quantization process and overhead. Assuming 5 bits of

dynamic range for each CQI value, extensive simulations of

channel variations suggest certain distributions for each

element of the compressed vector.

Table 1 shows the predefined offset values and the

required number of quantization bits for each element of the

compressed vector. Each element of the compressed vector

is represented by a fixed offset value and a Q-bit binary

word (0Æ2Q-1). As shown in the Table 1, a higher number

of bits is only required for the first two elements of the

vector that carry more information than the others. The

remaining elements can be represented by a fewer number of

bits.

The total number of required feedback bits is given by

LocationHaar NNN += . (12)

In Table 2, the total number of required bits for different

values of M is shown. In comparison to Best-M individual

CQI reporting scheme, Haar compression results in 25%,

26% and 32% saving for M=4, 5 and 7, respectively. Similar

comparison reveals considerable savings over DCT-based

schemes as well.

Elements of

compressed

vector

Offset

value

Range Quant bits

per

element

Number

of bits

y3(8) 3 3 Æ 16 4

y3(7) -1 -1 Æ 2 3

y3(6) -1 -1 Æ 1 2

M=3

y3(5) 0 0 Æ 2.5 2

NHaar=11

y3(8) 5 5 Æ 24 4

y3(7) 2 2Æ 9 4

y3(6) -1 -1 Æ 1 3

y3(5) 0 0 Æ 2.5 3

y3(4) -2 -2 Æ 2 2

M=5

y3(3) -2 -2 Æ 2 2

NHaar=18

Table 1 - Quantization information for different M values.

CQI feedback

scheme Nsb=25

M=3 M=4 M=5 M=7

Full Feedback 125 bits 125 bits 125 bits 125 bits

Best-M Average 22 bits 24 bits 26 bits 29 bits

Best-M

Individual

32 bits 39 bits 46 bits 59 bits

Haar Best-M

Individual

<20 bits 29 bits 34 bits 40 bits

Best-M DM 28 bits 32 bits 36 bits 43 bits

DCT

Significant-M

24 bits 31 bits 39 bits 53 bits

DCT

Partitioning NA

N1=3,N2=1,

34 bits

N1=4,N2=1,

43 bits

N1=6,N2=1,

57 bits

Table 2 - Overhead comparison of CQI feedback schemes.

V. DISTRIBUTED-HAAR CQI FEEDBACK SCHEME

Although the multipath channel is time-varying, in many

cases it preserves most of its frequency spectrum

characteristics over a finite period of time (i.e., the channel

coherence time). Therefore, the update interval of the full

channel does not need to be every sub-frame. In this paper,

we proposed a new CQI feedback scheme called distributed-

Haar to reduce the overhead feedback by exploiting this

characteristic.

The flow of the reporting mechanism can be summarized

as follows:

1. Divide the sub-bands into NG groups. Locations of the

groups are known in advance to both mobile users and

base station. The groups can be defined in any manner.

However, partitioning sub-bands into equal-distant

groups is a simple and efficient way to do the grouping.

2. At each Reporting Interval (RI), apply a best-M Haar

compression to the CQI values of one of the

groups.

Gsb NN /

3. Perform step 2 on the remaining groups in subsequent

reporting intervals to cover the whole cell bandwidth.

As a result of this approach, in every reporting interval, the

number of sub-bands is reduced from to .

Hence, this allows the mobile user to use a smaller M for

CQI reporting at each reporting interval. Figure 3 shows an

example of distributed-Haar compression for CQI feedback

for N

sbN Gsb NN /

sb=8 and NG=2.

Figure 3: An example of Distributed-Haar CQI Feedback.

For the purpose of illustration, we consider a system with

Nsb = 25, M = 5. For such a system, the Best-M individual

CQI reporting scheme with and without Haar compression

requires 46 bits and 34 bits overheads, respectively.

However, using the distributed-Haar scheme with NG =2, the

sub-bands can be divided into two groups (even and odd) of

12 and 13 sub-bands. Then, Haar compression is applied

with a smaller M of 3 to each group. Therefore, for CQI

reporting of odd and even sub-band groups we have

bits19811

bits20911

=+=+=

=+=+=

LocationHaareven

LocationHaarodd

NNN

NNN

(13)

Hence, the number of information bits in each partial

feedback is much lower than other schemes listed in Table 2.

In each partial feedback, the M best sub-bands and an

average CQI is reported to the base station. Given a lower

number of bits per report, the base station will have more

frequent updates of CQI than other reporting schemes.

VI. PERFORMANCE RESULTS

Parameter Assumption

Cellular Layout Hexagonal grid, 19 cell sites, 3

sectors per site

Inter-site distance (ISD) 500m

Number of transmit antennas at NB 1

Number of receive antennas 2

Distance-dependent path loss L=I + 37.6log10(.R), R in kilometers

I=128.1 – 2GHz

Lognormal Shadowing Similar to UMTS 30.03, B 1.41.4

Shadowing standard deviation 8 dB

Penetration Loss 20dB

Channel model Typical Urban (TU)

Antenna pattern (horizontal)

(For 3-sec. cell sites with fixed ant.

patterns)

( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞

⎜⎜⎝

⎛−= m

dB

AA ,12min

2

3θ

θθ

dB3θ = 70 degrees, Am = 20 dB

BS Antenna Gain plus cable loss 15 dBi

Carrier Frequency 2.0 GHz

System Bandwidth 10 MHz

RB bandwidth 180 KHz

Number of mobile users per Sector 10

Mobile user speeds of interest 3km/h, 15 km/h

Maximum Node B transmission

power

35 dBm

Mobile user Traffic Model Full Buffer

Noise Figure 9dB

Thermal noise density -174 dBm

Scheduler Proportional Fair

HARQ Asynchronous (Chase combining)

CQI measurement error Gaussian zero-mean error model

CQI averaging window 4 TTIs

CQI feedback delay 2 TTIs

CQI reporting interval (RI) 2, 4, 6 and 8 TTIs

Target BLER 10%

A. Simulation Methodology and Parameters

A system-level simulation using a proportional fair

scheduler was performed to evaluate the aforementioned

CQI reporting schemes in a system with a 10 MHz

bandwidth. In the downlink transmission Resource Block

(RB) grouping is assumed, where one CQI sub-band

contains

2 RBs. In the simulation a CQI granularity of 20 MCS levels

is used. The impact of CQI measurement delay and errors

are considered as suggested in [4] and [8]. The simulation

parameters are listed in Table 3.

Table 3 – Simulation parameters

B. Simulation Results

The performance metric of evaluating CQI feedback

schemes is the average sector throughput. For different CQI

reporting schemes including Best-M individual, distributed-

Haar, DCT Significant-M and DCT partitioning, the average

sector throughput performance is measured and compared

under different CQI reporting intervals via simulations.

The average sector throughputs for mobile user speeds of

3km/h and 15km/h are shown in Figure 3 and Figure 4,

1 2 3 4 5 6 7 8

1

2

3

4

5

6

7

8 t=i

t=i+1

Haar

Haar

Feedback t=i

Feedback t=i+1

respectively. Each graph demonstrates the performance of

various schemes against the required number of bits per

report. The required number of bits per report is evaluated

by dividing the corresponding number from Table 2 and

Equation (13) by the RI. As observed, the distributed-Haar

scheme outperforms other schemes around 10 bits per TTI

range for both cases (3 km/h and 15 km/h). At the speed of

15 km/hr, DCT-Significant has the best performance when

the number of overhead bits per TTI is small (< 7 bits per

TTI). However, around the range of 10 bits per TTI, the

distributed-Haar scheme yields the best performance and

outperforms Best-M individual, DCT partitioning and DCT

significant-M by 15.4%, 14.2% and 5%, respectively. At the

speed of 3km/h, distributed-Haar consistently provides the

best performance among all schemes over the whole range

of overhead bits per TTI. For example, the distributed-Haar

CQI reporting scheme provides 1.2%, 5.8%, 14.3%

throughput gains over Best-M individual, DCT partitioning

and DCT significant-M, respectively, at around 10 bits per

TTI.

For the same value of M, at low mobile user speed, e.g.

3km/h, the average sector throughput is insensitive to the

value of reporting intervals. This is because the CQI

reporting intervals of interest (2, 4, 6 and 8 TTIs) are much

smaller than the channel coherence time, which means that

0 5 10 15 20 25

12

13

14

15

16

17

18

number of overhead bits per TTI

A

ve

ra

ge

S

ec

to

r T

hr

ou

gh

pu

t (

M

bp

s)

3km/h

Best-5 Individual

DCT Partitioning (5-4-1)

DCT Significant(M=5)

Distributed-Haar(M=3)

RI=2msRI=4ms

RI=6msRI=8ms

RI=2msRI=4ms

RI=6ms

RI=8ms

RI=4ms

RI=2ms

RI=6msRI=8ms

RI=2msRI=4msRI=6msRI=8ms

Figure 3 - Average sector throughput vs. the number of overhead

bits per TTI at a mobile user speed of 3 km/h.

0 5 10 15 20 25

6

7

8

9

10

11

12

13

14

15

number of overhead bits per TTI

A

ve

ra

ge

S

ec

to

r T

hr

ou

gh

pu

t (

M

bp

s)

15km/h

Best-5 Individual

DCT Partitioning (5-4-1)

DCT Significant(M=5)

Distributed-Haar(M=3)

RI=2ms

RI=4ms

RI=6ms

RI=8ms

RI=8ms

RI=4ms

RI=6ms

RI=2ms

RI=2ms

RI=4ms

RI=6ms

RI=8ms

RI=2ms

RI=4ms

RI=6ms

RI=8ms

Figure 4 –Average sector throughput vs. the number of overhead bits per

TTI at a mobile user speed of 15 km/h.

the multipath channel is static during the reporting interval.

However, at higher mobile user speed, e.g. 15km/h, the

average sector throughput decreases remarkably with

increasing CQI reporting interval. This is because the CQI

reporting intervals of interest (4, 6, 8 and 10 TTIs) are

comparable to the channel coherence time, which means that

the multipath channel fluctuates during the reporting

interval. Large reporting intervals introduce inaccuracy to

the reported CQI and corresponding base station’s

scheduling, which in turns degrades the average sector

throughput.

VII. CONCLUSIONS AND DISCUSSIONS

In this paper we have addressed the CQI feedback

overhead issue by applying best-M Haar compression to

distributed groups of sub-bands. Simulation results show

that the distributed-Haar scheme achieves a more flexible

trade-off between the throughput performance and feedback

overhead compared with other CQI compression techniques

(e.g., Best-M individual, DCT-Partitioning and DCT

significant-M). At a reasonable CQI feedback payload (e.g.,

around 10 bits per TTI), the distributed-Haar scheme

provides throughput gains up 15.4%, 14.2% and 5% over

Best-M individual, DCT-Partitioning and DCT significant-M

feedback schemes, respectively. Excluding the significant-M

method that has the poorest performance at the low speed,

all the other investigated methods exhibit similar sensitivity

in sector throughput performance to the mobile speed.

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Lundevall, and S. Parkvall, "The 3G Long-Term Evolution - Radio

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[2] Young-June Choi; Kwang Bok Lee; Saewoong Bahk, "All-IP 4G

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[4] R1-071104, "System level evaluation of CQI compression schemes for

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[5] R1-062575, "Further Analysis on DCT based CQI reporting Scheme",

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[6] Minos Garofalakis. "Wavelet-based Approximation Techniques in

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[7] Colm Mulcahy, "Image compression using the Haar wavelet

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